I think the biggest problem people have when drawing with crayons is that they regress to being five years old again. They hold the crayon like they're coloring again, instead of applying it like a fine art medium. Another problem is that many people want to make it perform like colored pencils. While similar in application, they are quite different. You should not use crayons and expect them to behave like colored pencils. You'll be setting yourself up for disappointment.
Use Crayola. These are the best and have the best color saturation. Use a paper that will grip the color evenly. I like Stonehenge or illustration board. Have a good hand_held sharpener handy. Always try to keep a point on the crayon. This makes it go on more evenly. Apply the crayon in a professional manner. Just like you would any other fine art tool, use control and be deliberate. Don't become five years old again!